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\begin{document}
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\mainmatter % start of the contributions
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\title{Cell Assemblies as an Intermediate Level Model of Cognition}
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\author{Christian R. Huyck}
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\tocauthor{Christian R. Huyck (Middlesex University)}
\institute{Middlesex University, London, UK,\\
\email{C.Huyck@mdx.ac.uk},\\ WWW home page:
\texttt{http://www.cwa.mdx.ac.uk/chris/chrisroot.html}}
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\begin{abstract}
This chapter discusses reverberating circuits of neurons or Cell
Assemblies (CAs) derived from Hebb's \cite {Hebb} proposal.
It shows how CAs can quickly categorise an input and make a quick
decision when presented with ambiguous data. A categorisation
experiment with a computational model of CAs shows that CAs categorise
a broad range of patterns.
This chapter then describes how CAs might be used to implement the
primitives of an symbolic cognitive architecture. It also shows how a
system based on CAs is theoretically capable of fast learning,
variable binding, rule application, integration with emotion and
integration with the external environment.
CAs are thus an ideal mechanism for further research into both
computational and cognitive neural models. Our medium to long-term
plan for exploration of thought via CAs is described.
If humans use CAs as a basis of thought, then studying how biological
systems use CAs will provide information for computational models.
The reverse is also true; computational modelling can direct our
research activity in biological neural systems.
\end{abstract}
\section {Background and Introduction}
I want to start this chapter with an apology. This work is about how
humans (and other creatures) think. The claims often strike me as
arrogant. Discovering how people think has been a major problem of
philosophy for thousands of years. For me to say, ``we think because
of Cell Assemblies (CAs)'' is arrogant, and thus we apologise. The
statement is also currently backed by little evidence. I once heard
Herb Simon say ``if you work on an interesting problem, you will get
somewhere if you answer it.'' Understanding thought is important, and
CAs are crucial to our understanding of thought. So, I will continue
with the claim that we think because of CAs, show how they can
provide a sound model of thought, and provide some evidence.
Thought is extremely complex and perhaps the most complex thing that
we study. One way to decompose the problem of modelling thought is to
model it at different levels of granularity. For instance, Newell
divides cognition into levels by time \cite {Newell}. The biological
band is fastest and its primitive operations take place between
$10^{-4}$ and $10^{-2}$ seconds; the primitives in the cognitive band
function from $10^{-1}$ seconds to $10^{1}$ seconds, the rational band
from $10^{2}$ to $10^{4}$ seconds and the social band above that.
Models can be built at any level.
Each band is broken into three levels. The neural level, functioning
near $10^{-3}$, and the neural circuit level, functioning near
$10^{-2}$ seconds, are in the biological band. The deliberate act
level near $10^{-1}$ is in the cognitive band.
While models can be built at different levels, each level depends on
those below it. A model at the deliberate act level functions via certain
assumed primitive operations. It is assumed that these primitives can
be implemented in the lower levels.
Newell and other symbolicists have focused on the cognitive and
rational bands \cite {Laird}. These are the symbol processing levels.
Anderson's ACT* \cite {Anderson} system works at this level but also
integrates neural models as a means of showing human reaction and
performance times.
For instance, Newell bases his architecture on the deliberate act
level. The primitives are to assemble operators and operands, apply
the operator to the operands, and to store results. Additionally, the
system must support structures, input and output. Higher
levels are then built upon the deliberate act level.
Why does Newell select these primitives? Can we be sure that these are
the right primitives? While Newell has reasons for selecting these
primitives, there is no firm basis in the neural circuit level (the
level directly below the deliberate act level) that shows these things
working. If some basis could be found, then it would strengthen the
argument for these primitives. Moreover, it might have further
ramifications on higher levels. Currently, Newell's model is a
floating island; it is not firmly based on lower level structures.
Aside from the neural level, we have only indirect evidence of the
behaviour of all of the other levels. We can look at the firing and
activation of neurons, but we cannot see a rule being selected in the
operations level. Indirect evidence is useful; reaction times,
recognition times and other psychological evidence gives important
direction to studies of cognitive models. If a model does not match
the psychological evidence it is flawed. Still the size of the space
of possible models is huge (and probably infinite).
We are still working on models of neural behaviour but we do know a
great deal. Since we have this knowledge, we can use simplified models
of neurons to build neural circuits. This can inform higher level models
and reduce the size of the search space.
An interesting and somewhat neglected level is the neural circuit
level. The neural circuit level can bridge the gap between the neural
level and the cognitive band. If neural circuits can implement a model from
the cognitive band, then all of the models will be more firmly based.
While we have a good understanding of how neurons work, we have a
rather poor understanding of how neural circuits work. Direct analysis of
neural circuits is difficult because functioning circuits (in animals)
are very complex and our scanning techniques, including fMRI, PET and
electrodes are not very good at examining these circuits.
D. O. Hebb proposed a neural circuit model \cite {Hebb}, a
reverberating circuit of neural cells. Hebb called this reverberating
circuit a {\em Cell Assembly} (CA). Some physiological evidence for
CAs exists (e.g. \cite {Abeles,Spatz}).
While there has been a fair amount of work in psychology \cite
{Pulvermuller} and neuro-biology to show the existence of CAs, there
has been little computational modelling of CAs \cite
{Fransen,Hetherington,Huyck,Kaplan,Palm}. The computational modelling
has either been from a more abstract level than neurons \cite
{Kaplan}, has been of a very limited nature focusing on associative
memory \cite {Fransen,Hetherington,Huyck,Palm}.
The basic CA model is a network of neurons; each neuron connects to
other neurons, which in turn may come back (directly or indirectly) to
the original neuron. Some neurons (e.g. rods in the eyes) are not
parts of circuits; however, physiological studies show that most
neurons are in some sort of circuit \cite {Schuz}. That is, the human
brain is made mostly of circuits of neurons. Studying these circuits
is crucial to our understanding of thoughts.
While there is a considerable theoretical and physical body of evidence for CAs,
what exactly do CAs do? CAs have the following (theoretical) properties.
\begin{enumerate}{}
\item CAs recognise concepts.
\item CAs are composed of neurons.
\item Neurons may exist in more than one CA.
\item CAs are in working memory if and only if they are active.
\item A CA is a long-term memory item, and is formed by change in synaptic strength.
\item A CA remains in working memory for a short period ($ Local \> Half \> Interleaved \\
Number Runs\> \hspace{0.1 in} 300\> \hspace{0.1 in} 350\> \hspace{0.1 in} 1500 \\
A-A Corr.\> \hspace{0.1 in} 1\> \hspace{0.1 in} .9286\> \hspace{0.1 in} .9900 \\
B-B Corr.\> \hspace{0.1 in} 1\> \hspace{0.1 in} .9492\> \hspace{0.1 in} .9917 \\
A Self Corr.\> \hspace{0.1 in} .9970\> \hspace{0.1 in} .8821\> \hspace{0.1 in} .8621\\
B Self Corr.\> \hspace{0.1 in} .9734\> \hspace{0.1 in} .9562\> \hspace{0.1 in} .9386\\
A-B Corr.\> \hspace{0.1 in} -1\> \hspace{0.1 in} -.4973\> \hspace{0.1 in} -.9826 \\
\end {tabbing}
\vspace {-0.1 in}
The measurements are Pearson's product correlation coefficient. This
shows that the neurons activated when one A pattern is presented is
highly correlated with a different A pattern being presented (the A-A
row) and when two B patterns are presented (the B-B row). Both are
measured 5 cycles after the stimulus stops being presented.
Similarly, the A and B patterns are negatively correlated (the A-B
row). The pattern of activation is also maintained. The A and B self
correlation rows show the correlation between active neurons at cycle
5 and 20 cycles after the end of stimulus presentation.
This experiment shows that this model is capable of learning CAs over
the full range of exhaustive patterns. Local patterns, interleaved
patterns, and patterns which combined local groups and interleaved
groups all formed CAs. These patterns are unique, persist and are
reliably activated.
It takes longer to learn interleaved patterns, but they are
eventually learned. This is because a distance-biased network
helps localised CAs form. Distance-biasing acts as an attractor and
when a localised pattern is placed into that attractor, it is
easily learned. Patterns that fight the attractor can still
be learned but take longer, and are less successful.
Other experiments have been done, but this experiment shows that this
model is capable of recognising and categorising different types of
patterns. This is the primary function of CAs. From this, more complex
behaviour can be generated.
\section {Quick Activation of CAs}
The theory of CAs states that a CA is quickly activated \cite {Kaplan}.
This shows that slow neurons can quickly recognise an object.
\begin{figure}
\resizebox{\textwidth}{!}{\rotatebox{270}{\includegraphics{snoopy.eps}}}
\centerline{Figure 2.}
\end{figure}
Experiments using simple computational models of CAs shows
this to be the case \cite {Huyck}. This model shows that activation of
10 neurons can lead to activation of the entire CA of 200 neurons in
the next time step. A time step is meant to model 10 ms. of real
neural activity. This particular experiment is probably not viable
from a neurological standpoint as the size of the CA is very small.
However, it does show how quickly a few neurons can lead to activation
of many more neurons.
A real CA would probably cross several brain areas. However, it would
only take a few time steps (tens to hundreds of milliseconds) to
activate the entire assembly. Highly parallel activation compensates
for slow neural speed. Practically, it will be easy to get large
numbers of neurons activated within the speeds that are needed for
normal real-time performance.
Figure 2 shows the activation curve of a CA. At time 0, a stimulus is
presented to the network. Rapidly, a large percentage of the neurons
in the CA become activated and this is associated with recognition.
Stimulus may be removed or remain present. Some neurons in the CA are
active for quite some time meaning the CA can spread information,
strengthen itself (via the Hebbian learning rule) and remain in
short-term memory. Note that no neuron remains active for the whole
period; they become active, fatigue, recover and are reactivated by
other neurons in the CA.
\section {Quick Decision on Ambiguous Data}
A human brain must have millions of CAs, but our model networks are
much smaller. A given net may have several CAs in it, but only one or
a few should be active at a given time. What happens when a net is
presented with ambiguous data?
When ambiguous data is presented to a net, some of the neurons from
two separate CAs will be activated. These will tend to activate other
neurons in their own CAs. Since the two CAs have never been active
together and reside in the same area of a distance-biased network,
they will tend to inhibit each other. Thus a competition ensues
between the two ambiguous CAs. One CA wins, and the data is
recognised as an instance of that type of object.
\begin{figure}
\resizebox{\textwidth}{!}{\rotatebox{270}{\includegraphics{ambig.eps}}}
\centerline{Figure 3.}
\end{figure}
When the net is presented with ambiguous data it does take slightly
longer to recognise the object. This is due to the extra time needed
for competition. However, it should only take a few more cycles to
recognise the object, and thus is almost as fast as recognising an
object from unambiguous data.
Figure 3 shows the activation pattern of two CAs. Both get an initial
burst of activating neurons. Some of these neurons are inhibitory
neurons and inhibit neurons from other CAs, thus inhibiting the other
CA. The CA represented by the bold line loses the competition and
returns to its base firing rate. Of course this is all theory. We do
not know of any model of a CA that handles ambiguous data \footnote
{We are currently working on such an experiment based on the CANT
model and the results are promising.}.
%\section {The Necker Cube}
%The Necker Cube is clearly an ambiguous object. However, the earlier
%discussion of ambiguous objects shows that only one object is quickly
%chosen. The Necker cube ocillates between one interpretation and the
%other. Why is this?
%Fatigue and persistent ambiguous input.
%One never sees both interpretations at the same time.
\section {The Other Areas}
CAs categorise and they do it quickly. This chapter has described how
the CANT model does this. CAs also provide many other properties that
are very useful for a computational model of intelligence. They are
robust, they learn in context and they enable synchronisation of
neural firing. Additionally, they provide an excellent landmark for
asking questions about modularity and timing.
Like most ANN architectures, CAs are robust. Loss of neurons might
even strengthen a given CA. Since a CA is composed of a suite of
neurons, it can handle the loss of neurons; new neurons can be added
and incorporated into CAs. The dynamics of CAs recruiting new neurons
and fractionating into multiple CAs is not well understood, but the
process must be robust.
CAs learn in context. The CA learning mechanism is unsupervised. A
given network will spontaneously create CAs based on the input that is
seen. Thus all learning is in context. This may lead to unforeseen
connections between concepts, but those connections are based on the
input that has been presented.
CAs are self synchronising. Neurons in a CA tend to fire in a similar
pattern \cite {Palm}. Thus CAs actually act as a synchronising
mechanism. The mechanism also leads to a number of questions about
how CAs could work together. There are questions about variable
binding \cite {Fujii}; co-operating CAs may be bound together by
synchronisation. How is this done? How do CAs combine into larger
structures like sequences and cognitive maps \cite {Kaplan2}?
CAs also provide a landmark for questions of modularity. Braitenberg
\cite {Braitenberg} notes that the brain is largely a uniform mass of
neurons. CAs span brain areas \cite {Pulvermuller}. This enables
cross modular co-operation, yet intra-modular specialisation. A
working CA model could explore lots of questions about modular
communication.
Finally, animals have to do things by a certain time. CAs must be able to
function under deadline. CAs function rapidly but they still show no way
to solve problems by a certain time. CAs provide a mechanism for building
complex systems to solve problems. If CAs can be used to generate a goal
mechanism with interrupts, then the deadline problem can be addressed.
\section {An Intermediate Level Model}
A good intermediate level model\footnote {a neural circuit model} would
support the primitives of Newell's deliberate act level \cite {Newell}:
\begin{enumerate}{}
\item Get Input
\item Select Operators and Operands
\item Apply the Operator
\item Store the Results
\item Generate Output
\item Support Structures
\end{enumerate}
The CANT model already has demonstrated support for input, operator
and operand selection, and storing results. It holds promise for
operator application, output generation and more complex structures.
The CANT model supports direct input. In biological systems, sensory
organs activate neurons. In a CANT network, we could connect sensory
organs directly to the neurons. The sensory system and underlying
neural system are very complex and well studied, and the neural system
is largely compatible with the CANT model.
Operators and operands can be selected based on current input and prior input.
CA activation can be thought of as operator and operand selection; an operator
and operands are selected if and only if their CAs are activated.
Results are stored by either putting them in working memory or in
long-term memory. To put them in working memory an existing CA has to
be activated. To put them in long-term memory, a new CA must formed.
This is done by changing synaptic weights.
Output can be generated by effectors. Like biological input,
biological output is done by the body. Muscles move and vocal chords
vibrate. The underlying neural control mechanisms, though not entirely
understood, are well studied. Again, these are compatible with CA
theory and CA based controllers.
Structures are more complex for CAs to generate and have many of the
questions in which we are currently interested. How do CAs build, for
instance, a verb frame? Weak connections between CAs must be quickly
learned via the Hebbian learning mechanism. We do not currently have
a functioning computational model of this process, but this is in our
medium term plans.
Operators are more complex in a CA model. Simple operators like {\em
store} have already been implemented. More complex operators like
move forward or multiply two numbers are more difficult. These
complex functions may be implemented by decomposition into primitives.
Primitive operators are done by the output mechanisms and storage
mechanisms described above. Still the functions need to compose these
primitives via CAs. This composition is done via complex structures
like sequences and cognitive maps. As before, these are learned by
creating weak links to combine CA primitives.
We like Newell's division into levels and are particularly interested
in Soar; thus we have focused our argument in that direction.
However, there is nothing sacred about the Soar model. Newell's
deliberate act primitives may turn out to be wrong. What is important
is that the higher level behaviours that can be built on the
deliberate act primitives can be built from CAs. If it turns out that
humans build the behaviours differently, CAs should be flexible enough
to account for that behaviour. If we can implement Newell's system
than CAs will have implemented a strong system.
Additionally, the CANT model may support other aspects of behaviour
including emotion, attention, fast learning and forgetting. Emotion
can be incorporated using a pleasure/pain mechanism. This interacts
particularly well with a Soar-like goal mechanism. Unappealing and
dangerous CAs are associated with (connected to) pain, a pleasurable
CAs to pleasure. This can direct behaviour.
Attention can be explained with a more global mechanism. CA theory,
as presented so far, is entirely localist. There is no global
mechanism. However, CAs are connected to other CAs. An attention
area or cognitive map could be connected to all other areas. It could
focus attention via a global inhibitory mechanism. This would allow
only the most active CA to remain active.
Fast learning may be accomplished by reverberation, support from
cognitive maps, and attention. These aids can support more neural
pair coactivations and thus quick strengthening of connections.
We also forget. CAs can account for this. Forgetting is done by a
change in synaptic strengths. Core concepts, CAs, are rarely
forgotten (you do not forget what a dog is). This is because the CAs
occasionally become active and their synaptic strength is reinforced.
Connections between concepts are more likely to be forgotten because
they are initially weaker and these connection are also used to
connect other CAs.
Finally, the CANT model supports a blackboard like architecture \cite
{Hayes-Roth,Reddy}. CAs consist of neurons that are closely connected
but connections to other CAs exist. This means that information from
a wide range of CAs may be brought to bare on a single problem.
A well known example of a blackboard system is the Hearsay speech
understanding system \cite {Reddy}. Hearsay consists of several
subsystems. Each subsystem can communicate to other subsystems via a
blackboard. A special subsystem chooses which subsystem will function
next based on which has sufficient information to function. In a CANT
blackboard, the architecture would decide which subsystem or
subsystems would function based on enough information being available.
Similarly information is exchanged via neural activation.
In traditional software systems we break the system into subsystems or
into components. This facilitates engineering. In the brain, this
really does not happen. Despite physiologists division into brain
areas, each area is closely connected to other areas. This whole
system is tightly coupled. This tight coupling may not facilitate
engineering, but the brain was not engineered.
Existing CA systems are associative memory systems; this includes the
experiments described in this chapter. What is needed is a model that
can combine CAs in an interesting way \cite {Ivancich}.
Von der Malsberg \cite {Malsberg} proposes dynamical connections as a
variant that is much more flexible than standard CA theory. CAs are
bound together via synchronous firing. This enables new concepts like
{\em blue square} to be formed quickly and temporarily from primitive
concepts like {\em blue} and {\em square}.
An unappealing alternative to this is that variable binding is done
by the change of synaptic strength. This is more tenable when overlapping
set coding \cite {Wickelgren} is considered. A given neuron participates in
more than one CA. So, a given neuron might participate in the {\em blue}
CA and the {\em square} CA. When the two CAs are coactivated, a new {\em
blue square} CA is formed. This is unappealing because of learning
time constraints and forgetting.
However, a middle ground exists. CAs are formed in the traditional
way and represent a ``strong force'' (e.g. {\em square} and {\em
blue}). Variable binding is done via synchrony and is a short term
effect just like CA activation is a short term effect. If the binding
is important or repeated, Hebbian learning leads to an association
between CAs; this is a ``weak force''. These weak forces are
available for sequences, hierarchies and cognitive maps of CAs. This
``weak force'' is facilitated by overlapping set coding. This may
be similar to the SMRITI system \cite {Shastri}.
The important point is that both synchronous firing and overlapping
set coding are compatible with CAs in general and the CANT model
specifically. Synchronous firing emerges from the activation of
neurons \cite {Palm}. Overlapping set coding also emerges from the
input and learning mechanisms.
\section {Future Work}
The long-term goal of this work is to move from neural models of
categorisation to neural models of processing. Currently, we are
working on a model of categorisation and associative memory. This
work duplicates, and hopefully extends, existing computational CA
models.
Next we hope to model interactions of CAs. This includes competition
amongst CAs, hierarchies of CAs, sequences of CAs, and maps of CAs.
This will be done via overlapping set encoding and synchronous firing
patterns.
Variable binding can lead to rule activation. If {\em A} and {\em B}
are active, then complete the pattern and activate C. Rule activation
provides the basis for traditional symbolic architectures. One
popular symbolic cognitive architecture is Soar. It can be described
as an expert system, with goals, operators, operator subgoaling and
chunking. If all of these can be implemented in a CA based system,
then CAs will have provided an intermediate level for cognitive
modelling.
A system like CA-Soar would escape from the symbol grounding criticism
of Fodor and Pylyshyn \cite {Bechtel}. It would direct
psycho-neurological research. It would provide a plausible model for
thought and thus for real Artificial Intelligence.
Implementing this set of performances is not straight forward, but one can
easily imagine that it is possible. We suspect that this CA-Soar model would
be more dependent on categorisation than current Soar programs. This reflects
the associative nature of the brain.
\section {Discussion and Conclusion}
This chapter has shown that CAs can be used to classify a wide range
of patterns. It has also argued that CAs can be expanded to account
for variable binding, hierarchy and cognitive maps. This
functionality will enable CAs to provide the primitives for Newell's
deliberate act level. Thus CAs can form a bridge between the
relatively solid knowledge that we have of neural behaviour to the
highly developed work we have on symbolic cognitive architectures.
One may ask why CAs have not yet been used to build a symbol system.
It is likely that the recent interest in connectionist systems \cite
{Sun} has laid new foundations for this work. Additionally,
computational speed has only recently enabled large neural models to
be run.
CAs can be used to store memories that are based in reality. They can
solve the symbol grounding problem. Current computer memory can store
the sentence ``the cat chased the mouse''. When asked ``what was
being chased'' it can respond, but it can not respond to ``why was he
being chased''.
Traditional computer memory is great for number crunching. CA models
may be faster than biological CAs but will still be slower than
Von Neumann architectures. CAs however function in context and can
generate statistically reasonable answers from little data. They
will function better than Von Neumann architectures in AI tasks like
Natural Language Processing and Decision Support Systems.
This book is derived from the Third International Workshop on Current
Computational Architectures Integrating Neural Networks and
Neuroscience. The key question for the workshop was {\it What can we learn from
cognitive neuroscience and the brain for building new computational
neural architectures?} In relation to this chapter, we would like to
break that question into two questions: \\
1. {\it What can we learn from cognitive neuroscience and the brain for building
CAs?}\\
2. {\it What can we learn from CAs for building new computational neural
architectures?}
It is simple to say what the brain can tell us about CAs. The way
each neuron behaves, and the way they are connected in the brain is
the way CAs should behave. Any CA model will be simplified as
modelling a single neuron is very complex. Perhaps we can simplify
the model by simply modelling changes in neural activation in discrete
steps and learning by changes of strength. This is not as robust as
modelling neural activation continuously with ionic transfer between
neurons, and modelling changes of strength by changes in axonal
radius, myelination and geometric properties of the synaptic
cleft. This simplification makes the model run faster which should
enable us to model the large number of neurons needed for CAs. Still
it is a simplification and, as such, may miss important data.
It is more difficult to say what CAs can tell us about building new computational
neural architectures. CAs are models for concept storage. They can
solve the symbol grounding problem. Perhaps the most interesting question is in what
way can CAs work together.
At heart, CAs are a model for data storage. They have several advantages that
could be transferred to other models. They remain active for a certain period of
time. They are a model for both long and short-term memory. They can be used
to choose between equally likely solutions. It is the reverberating activity that
makes this model different from most existing ANN models.
Further studies to show how CAs can store more complex structures and
process data are important. The class of reverberating circuits is
large and we have done little in studying this class. Clearly, the
brain is not just a bunch of CAs. For instance, non-local effects
\cite {Katz} probably are important. However, CAs are crucial and we
need to understand them and how they work.
Using CAs as a basis for more complex phenomena puts us on reasonably
solid ground for future exploration of how the brain works at more
complex levels. This in turn leaves us with a better understanding of
intelligence and thought.
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\end {document}